On Thursday, swimmers at Newcastle city pool will take the plunge for the last time before it is closed as part of a severe cuts programme designed to save £100m over three years.

The move is just one of hundreds of cuts to sports and leisure programmes and facilities across the country – cuts the government has admitted could undermine its Olympic legacy promises.

Guardian research reveals a disparate picture, of deep cuts of over 40% to sports and leisure budgets in some parts of the UK and relatively minor ones in others. The government has now conceded the cuts may put at risk promises that the London 2012 Olympics would leave a legacy of increased sports participation and a healthier nation.

Among those councils planning to cut sports and leisure budgets by over a fifth between 2011-12 and 2013-14 are Swindon, Wigan, Walsall, Essex, South Tyneside, Oldham, Liverpool and Manchester.

In Sheffield a group campaigning to save a leisure centre that is home to a 25-metre pool and a thriving gymnastics club – one of the sports under most pressure following the Games, with lengthy waiting lists of enthused children unable to find facilities and coaches – is considering the case for a judicial review.

In Wigan, a reduction of 41% over two years is part of a drive to save £18.8m over the next 12 months. It has resulted in a range of cuts, including the withdrawal of free swimming for people over 65 and those under 16, to save £106,000 a year.

The situation in Wigan is complicated by the fact that its arm's-length leisure trust, which has had its budget cut from about £16m to £10m over three years, also funds libraries, parks, cemeteries and arts projects, so separating the impacts on sports and recreation is difficult. It said it had largely been able to limit the frontline impact to axing free swimming and transfering two pools to community ownership.

Chris Ready, Wigan council's portfolio holder for leisure, said: "We have a proud history of investing in sport in Wigan borough but the government's cuts have made it more and more difficult for us to maintain all of our facilities and services. Thankfully, the passion for sport that we and our residents both share means we have managed to hand over two of our smaller swimming pools to local community groups. We have also had to make some very tough decisions in other areas of the leisure and culture portfolio to safeguard the services that our most vulnerable residents rely on."

Many councils that retained free swimming when funding for a national scheme was withdrawn in 2010 have now been forced to reconsider.

In Manchester, a city council that perhaps more than any other in the country has used large-scale sports projects to drive regeneration, the budget is being cut by 21%.

The city council, battling to address a funding shortfall of £80m over the next two years, had proposed the immediate closure of a total of four swimming pools in Broadway, Levenshulme, Miles Platting and Withington. The latter has since been given a stay of execution and it promises three new pools will have opened by 2015.

In Liverpool, the future of two municipal golf courses, in Allerton and Kirkby, home to junior coaching and school outreach programmes, will be in serious doubt if a private operator cannot be found.

As with other cuts to libraries and arts projects, Newcastle's Labour-controlled council says it has no choice but to close the well-used pool as part of its £100m cuts package, and points to alternative facilities nearby, despite a desperate rearguard action that included a "swim-in".

Local campaigners across the country fear that there will be a second wave of casualties if facilities that are passed to local trusts or commercial operators end up unable to survive without subsidy. There are also concerns about the maintenance of pitches and playing fields.

It is not only facilities that are being hit. In Newcastle, the number of staff employed in its Raising Participation team, its sports health and fitness specialists and "sport specific delivery teams" are being reduced as part of plans to save more than £1m over three years.

"There is absolutely a risk [to the Olympic legacy] if local authorities cut sports budgets," he said. "It is not going to destroy the legacy but it is not going to help it in any shape or form.

"I'll be pretty brutal about this: we were worried there were Labour authorities that were quite deliberately closing arts facilities and shutting sports facilities in order to make a political point, particularly in big cities in the north."

Labour forcefully rejects the claim. It has produced an analysis of budgets according to which its councils last year cut sport and leisure budgets by 6%. That figure compares, it says, with cuts of 11% in Conservative-controlled authorities and 17% in Liberal-Democrat-run councils.

"If we are to deliver a sustainable sports legacy then this government has to understand that it has a strategic role to play and should be working with local authorities to minimise the impact of cuts on sports services and facilities," said the shadow sports minister, Clive Efford. "It is clear that this government does not consider that it has any form of strategic role whatsoever."

Since before the Olympics, there have been dire warnings that cuts will fall disproportionately on sport and leisure funding because those budgets are not protected by statute, despite a genuine desire among most councils to capitalise on enthusiasm generated by the Games.

The former sports minister Richard Caborn considers the landscape to be "bleak" and the former British Olympic Association chairman Lord Moynihan, a former Tory sports minister, has also warned the cuts could undermine any gains from the Olympics.

The recent decision by Sheffield city council to close Don Valley athletics stadium, despite the protests of the Olympic gold medallist Jessica Ennis and her coach, Toni Minichiello, made national headlines. But to those in Sheffield, a more worrying proposal is the closure of the popular Stocksbridge leisure centre.

Isobel Bowler, the cabinet member for culture, leisure and sport at Sheffield council, said she had received vastly more complaints about the Stocksbridge decision than the high-profile Don Valley one. A group representing the leisure centre, which has until next month to come up with a way of surviving without £400,000 a year in government subsidy, is considering a judicial review.

The Don Valley decision has divided opinion. Some, including the London 2012 chairman and government legacy adviser, Lord Coe, who grew up in the city, concede that continuing to operate a facility that requires £700,000 of public subsidy a year to operate and £1.6m of urgent maintenance is difficult to justify.

Instead, Coe told the Guardian, the council must ensure that plans to upgrade the nearby Woodbourn track, to provide a home for the athletics clubs housed by Don Valley and other community users, are of a high enough standard. That proposal was, he said, "entirely predicated on a properly resourced replacement track and field facility in Sheffield".